You have 6 cups of sugar. It takes 1 cup of sugar to make 24 cookies. The function c(s) = 24s represents the number of cookies, c, that can be made with s cups of sugar. What domain and range are reasonable for the function?

These are my options:
domain: 1<s<6
Range: 24<c(s)<144

domain: 0<s<6
range: 0<c(s)<144

domain: 24<c(s)<144
range: 1<s<6

domain: 0<c(s)<144
range: 0<s<6

It is hard for me to get the domain and range of this problem. Thanks.

To determine the reasonable domain and range for the given function c(s) = 24s, let's consider what the variables represent in the context of the problem.

In this problem, "s" represents the number of cups of sugar, while "c(s)" represents the number of cookies that can be made using that amount of sugar.

The domain of a function represents all the possible values for the input variable (in this case, "s"). Since you have 6 cups of sugar, the maximum amount you can use is 6 cups. Therefore, the reasonable domain for this function should be 0 < s ≤ 6 (or alternatively, 0 ≤ s ≤ 6).

The range of a function represents all the possible values for the output variable (in this case, "c(s)"). Since each cup of sugar can yield 24 cookies, the minimum number of cookies would be 24 * 0 = 0. However, there is no maximum constraint given in the problem for the number of cookies that can be made. Therefore, the reasonable range for this function should be 0 < c(s) (and there is no upper limit, so no need to specify a maximum value in the range).

With this in mind, among the provided options, the correct choice is:
Domain: 0 < s < 6
Range: 0 < c(s)